We ran our Chicago office from the Oak Park Public Library for something like 5-6 months. There was a credible coffee shop on the first floor, and the library allowed drinks. Free wi-fi. Desks. For meetings, we could book private study rooms for 1-2 hours on almost no notice.

The only real downside to the library was that you couldn't get on the phone during the day without going outside.

The nicest thing about the library is that it works well exactly up to the point where you need and can afford an office.

Unlike the coffee shops, which mostly lose out by being packed full of people who buy one cup of coffee per hour, the library basically exists for the purpose of providing a quiet space for knowledge work. You fund it with your taxes. Library architecture in most metro areas is excellent. You should work out of the library.